Geoscience Reference
In-Depth Information
7.3 Derived Evapotranspiration Models
7.3.1 Equilibrium Evaporation
If we consider an extensive surface well supplied with water, we would expect that at
a certain stage the air above the surface would become saturated with water vapour.
As a result the aerodynamic term of the Penman equation would become zero and
the evaporation from the surface would be equal to the radiation term only. If energy
would continue to be supplied, the evaporation would continue and one would intui-
tively expect the air to become oversaturated (i.e.,
e
a
> e
sat
(
T
a
)) due to the continuous
supply of water vapour. One could imagine this scenario to occur, for instance, when
air is advected over the ocean over long distances.
However, the surface supplies not only water vapour to the air, but heat as well:
s
=
( )
−
+
*
1
γ
. Hence the air temperature increases so that
e
sat
(
T
a
) increases
as well. It can be shown that the increase of
e
a
and
e
sat
(
T
a
) occurs at the same pace so
that
e
a
-
e
sat
(
T
a
) remains zero once saturation is reached.
This remaining evaporation is called the equilibrium evaporation:
H
QG
s
s
(
)
LE
v q
≡
+
QG
*
−
(7.17)
s
γ
In practice, however, it appears that the air above wet surfaces hardly ever becomes
completely saturated.
4
This lack of saturation of the air is due to the fact that the atmo-
spheric boundary layer (ABL), is not a closed box. The air above the ABL is warm
and dry. Hence, at the top of the ABL warm and dry air is entrained from the free
atmosphere into the boundary layer leading to a warming and drying of the bound-
ary layer (see
Figures 3.1
and
3.2
). This entrainment of dry air is equivalent to a loss
of humidity
from
the boundary layer (see
Figure 7.6
). This drives the water vapour
content away from saturation. As a result, the aerodynamic term of the Penman (or
likewise Penman-Monteith) equation always plays a role.
5
Question 7.8:
Consider the situation in the right part of
Figure 7.6
.
a) Explain the difference in the development of the water vapour pressure with the case
with
a lid (no loss of water vapour at the top, left part of
Figure 7.6
).
b) In
Figure 7.6
the lux of water vapour at the top of the box is sketched to be equal
at all
x
-locations. Explain that the lux in reality will change with location (and how
does it change?).
4
If
saturation occurs (e.g., fog formation), this will not be due to evaporation from the underlying surface only, but
some form of cooling or advection of moisture must play an additional role.
5
De Bruin (
1983
) was one of the irst to describe quantitatively the importance of the ABL on surface
evapotranspiration.
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